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International Journal of Technology Enhancements and Emerging Engineering Research (ISSN 2347-4289)
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IJTEEE >> Volume 1 - Issue 4, November 2013 Edition



International Journal of Technology Enhancements and Emerging Engineering Research  
International Journal of Technology Enhancements and Emerging Engineering Research

Website: http://www.ijteee.org

ISSN 2347-4289



On Application Of Matlab To The Motion Of A Finitely Damped String On Sobolev Spaces

[Full Text]

 

AUTHOR(S)

Egbuhuzor Udechukwu P., Ugbene Ifeanyichukwu, EzeEverestus O

 

KEYWORDS

Keywords and phrases: motion, Sobolev space, mechanical system, vibrations, damped strings, plucking technique, nylon and steel strings. 2010 mathematical subject classification: 70E15, 70E18, 70F25

 

ABSTRACT

ABSTRACT: The problem of vibrations of plucked strings was investigated. The objective is to determine the vibrational behaviour of a guitar with nylon and steel strings. The derived Newton's second law of motion [7] with damping coefficient was used and the equation of the form -T(x) sin⁡θ+T(x+∆x) sin⁡β-ω∆xU_t=mU_tt . . . (1) Was considered. The method of separable variable was applied and we obtained U_xx-KU_t= 1/C^2 U_tt . . . (2) The result shows that nylon strings decay mainly as a result of internal damping in the strings while steel strings decay due to air viscosity. Therefore we conclude that nylon strings are under less tension than steel strings [5].

 

REFERENCES

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[3]. G. Kelly: Fundamentals of Mechanical Vibrations; the University of Akron 2, 92-107 (1993)

[4]. N.C Pickering: Physical Properties of Violin Strings, Catgut Acoust. Soc. 44, 6-8 (1985)

[5]. R. Storjohann: A Mathematical Model of a guitar string,(2006)

[6]. T. D Rossing: Acoustics of Percussion instruments- Part II, the physics Teacher; 15,278-288 (1977)

[7]. V.E Howel and L.N Trefethen: Eigen values and musical instruments. Journal of comparative and applied mathematics; 135, 23-40 (2001)